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/** @file Implementation of Path::extrema()
*/
/* An algorithm to find the points on a path where a given coordinate
* attains its minimum and maximum values.
*
* Authors:
* Rafał Siejakowski <rs@rs-math.net>
*
* Copyright 2022 the Authors.
*
* This library is free software; you can redistribute it and/or
* modify it either under the terms of the GNU Lesser General Public
* License version 2.1 as published by the Free Software Foundation
* (the "LGPL") or, at your option, under the terms of the Mozilla
* Public License Version 1.1 (the "MPL"). If you do not alter this
* notice, a recipient may use your version of this file under either
* the MPL or the LGPL.
*
* You should have received a copy of the LGPL along with this library
* in the file COPYING-LGPL-2.1; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
* You should have received a copy of the MPL along with this library
* in the file COPYING-MPL-1.1
*
* The contents of this file are subject to the Mozilla Public License
* Version 1.1 (the "License"); you may not use this file except in
* compliance with the License. You may obtain a copy of the License at
* http://www.mozilla.org/MPL/
*
* This software is distributed on an "AS IS" basis, WITHOUT WARRANTY
* OF ANY KIND, either express or implied. See the LGPL or the MPL for
* the specific language governing rights and limitations.
*/
#include <2geom/curve.h>
#include <2geom/path.h>
#include <2geom/point.h>
namespace Geom {
/** Returns +1 for positive numbers, -1 for negative numbers, and 0 otherwise. */
inline static float sign(double number)
{
if (number > 0.0) {
return 1.0;
} else if (number < 0.0) {
return -1.0;
}
return 0.0;
}
/** @brief Determine whether the d-coordinate increases or decreases at the given path time.
*
* @param path A path.
* @param time A forward-normalized time on the given path.
* @param d The coordinate about which we want to know whether it increases.
* @return +1.0 if the coordinate increases, -1.0 if it decreases, 0.0 if it remains constant.
*/
static float find_direction_of_travel(Path const &path, PathTime const &time, Dim2 d)
{
if (time.t == 0.0) { // We're at a node point
if (time.curve_index == 0) { // Starting point of the path.
if (path.closed()) {
return sign(path.initialUnitTangent()[d] + path.finalUnitTangent()[d]);
} else {
return sign(path.initialUnitTangent()[d]);
}
} else if (time.curve_index == path.size()) { // End point of the path.
if (path.closed()) {
return sign(path.initialUnitTangent()[d] + path.finalUnitTangent()[d]);
} else {
return sign(path.finalUnitTangent()[d]);
}
}
// Otherwise, check the average of the two unit tangent vectors.
auto const outgoing_tangent = path.curveAt(time.curve_index).unitTangentAt(0.0);
auto const incoming_tangent = path.curveAt(time.curve_index - 1).unitTangentAt(1.0);
return sign(outgoing_tangent[d] + incoming_tangent[d]);
}
// We're in the middle of a curve
return sign(path.curveAt(time.curve_index).unitTangentAt(time.t)[d]);
}
/* Find information about the points on the path where the specified
* coordinate attains its minimum and maximum values.
*/
PathExtrema Path::extrema(Dim2 d) const
{
auto const ZERO_TIME = PathTime(0, 0);
// Handle the trivial case of an empty path.
if (empty()) {
auto const origin = initialPoint();
return PathExtrema{
.min_point = origin,
.max_point = origin,
.glance_direction_at_min = 0.0,
.glance_direction_at_max = 0.0,
.min_time = ZERO_TIME,
.max_time = ZERO_TIME
};
}
// Set up the simultaneous min-max search
Point min_point = initialPoint(), max_point = min_point;
auto min_time = ZERO_TIME, max_time = ZERO_TIME;
unsigned curve_counter = 0;
/// A closure to update the current minimum and maximum values.
auto const update_minmax = [&](Point const &new_point, Coord t) {
if (new_point[d] < min_point[d]) {
min_point = new_point;
min_time = PathTime(curve_counter, t);
} else if (new_point[d] > max_point[d]) {
max_point = new_point;
max_time = PathTime(curve_counter, t);
}
};
// Iterate through the curves, searching for min and max.
for (auto const &curve : _data->curves) {
// Check the starting node first
update_minmax(curve.initialPoint(), 0.0);
// Check the critical points (zeroes of the derivative).
std::unique_ptr<Curve> const derivative{curve.derivative()};
for (auto root : derivative->roots(0.0, d)) {
update_minmax(curve.pointAt(root), root);
}
curve_counter++;
}
auto const other = other_dimension(d);
return PathExtrema{
.min_point = min_point,
.max_point = max_point,
.glance_direction_at_min = find_direction_of_travel(*this, min_time, other),
.glance_direction_at_max = find_direction_of_travel(*this, max_time, other),
.min_time = min_time,
.max_time = max_time
};
}
} // namespace Geom
/*
Local Variables:
mode:c++
c-file-style:"stroustrup"
c-file-offsets:((innamespace . 0)(inline-open . 0)(case-label . +))
indent-tabs-mode:nil
fill-column:99
End:
*/
// vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:fileencoding=utf-8:textwidth=99 :
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